In a mixing bowl, whisk together the Dijon mustard and the vinegar. Slowly drizzle in the olive oil while whisking, this will form an emulsion. Instead of a whisk, a blender will do the job equally as well (just be sure to rinse out the margaritas). Season with the salt and pepper and place on the side for later use.
Season the onion slices with salt and black pepper. Drizzle the slices liberally with olive oil and balsamic vinegar.
Onto your hot and seasoned grill, place the onions in a single layer on the grill. The onions should begin to caramelize and be ready for flipping in about 3 minutes. Don’t fiddle with the onions, let them be. Once they have caramelized, use a spatula and flip them over. Grill for another 3-4 minutes. They should be well caramelized on both sides and softened. Put the cooked onions aside, and repeat the process until they are all grilled.
While still warm from the grill, toss the onions with the herbs, arugula and the dressing. Serve immediately.